101. The Golden Proportion, Beauty, And Dental Aesthetics Device for design, study of beauty in nature, art, science http://www.goldenmeangauge.co.uk/golden.htm

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102. Unfold The Golden Rectangle - Start 1, 1 The golden Mean NEXT Unfold thegolden Rectangle Start. Please Note! http://www.vashti.net/mceinc/unfold0.htm

Unfold the Golden Rectangle - Start Please Note!

103. Irrational Number 4 The golden mean satisfies the equation x 2 x - 1 = 0, so its continued fraction Itsconvergents are 1, 2, 3/2, 5/3, 8/5, , the ratios of consecutive http://www.ams.org/new-in-math/cover/irrational4.html

The most irrational number The most irrational number The most irrational number turns out to be a number already well known in geometry. It is the number g = ( which is the length of the diagonal in a regular pentagon of side length 1. This number, known as the "golden mean," has played a large role in mathematical aesthetics. It is not clear whether its supreme irrationality has anything to do with its artistic applications. The golden mean satisfies the equation x - x - 1 = 0, so its continued fraction expansion is the simplest of all: g = 1 + 1 1 + 1 1 + 1 1 + etc. Its convergents are 1, 2, 3/2, 5/3, 8/5, ... , the ratios of consecutive Fibonacci numbers. How well are these convergents approximating g? Here are the first few E/M ratios: convergent E/M c = 1/1 1.382 c = 2/1 .8541 c = 3/2 1.055 c = 5/3 .9787 c = 8/5 1.008 c = 13/8 .9968 c = 21/13 1.001 c in Hurwitz' theorem cannot be improved!) So the golden mean can never have a rational approximation as good as 22/7 was for or even as good as 7/5 was for On to next irrational page.

104. IOnOne | Art | Architecture | Golden Section The golden Section by Hans Walser The golden Section. ·, by Hans furtherextensions. read more . The golden Section by Hans Walser. http://www.ionone.com/arcgolds.htm

art architecture painting music startup.file golden section divine proportion, golden ratio, PHI construction search for golden section Divine Proportion by Luca Pacioli golden section by Runion A Study in Mathematical Beauty Mathematical History Golden Number Fibonacci Ratios Geometry: Euclid and Beyond Essays on Number in Architecture link@ Technical University Hamburg-Harburg proportion : Claude Debussy The Golden Section by Hans Walser Since antiquity, the Golden Section has played a significant role in many parts of geometry, architecture, music, art, and philosophy. But it also appears in the newer domains of technology and fractals. In t his way, the Golden Section is no isolated phenomenon but rather, in many cases, the first and also the simplest non-trivial example in a sequence of generalizations leading to further developments. It is the purpose of this book, on the one hand, to describe examples of the Golden Section, and on the other, to show some paths to further extensions. read more da Vinci proportions The Last Supper Vitruvian Man (The Proportions of the Human Figure), 1490

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